Q: What does IP Maths Notes (Lower Sec, Year 1-2): 08) Trigonometry in Right Triangles cover? A: Apply sine, cosine, and tangent to height-distance problems, bearings, and angles of elevation with calculator and non-calculator techniques.
Trigonometry unlocks height and distance tasks across science and geography contexts. Become fluent with ratios, inverse functions, and diagram interpretation.
Given right triangle with angle θ=37∘ and hypotenuse 12 cm, find the opposite side.
sin37∘=12opp⟹opp=12sin37∘≈12×0.601=7.21cm.
Worked example - Finding an angle
Opposite side 5 cm, adjacent side 8 cm. Find θ.
tanθ=85⟹θ=tan−1(85)≈32.0∘.
2. Exact values and surds
Memorise sin30∘=21, cos45∘=22, tan60∘=3.
Use rationalisation to present answers cleanly: if sinθ=23, then θ=60∘ or other equivalent angles depending on context.
3. Angle of elevation/depression
Angle of elevation: measured upwards from horizontal.
Angle of depression: measured downwards from observer to object.
Worked example - Two-point observation
A drone lifts off and reaches a point where the angle of elevation from a student 50 m away is 35∘. What is the drone height?
tan35∘=50h⟹h=50tan35∘≈35.0m.
4. Bearings and composite paths
Bearings measured clockwise from north. Break vectors into horizontal/vertical components using cosine and sine, then recombine with Pythagoras.
Preview: sine and cosine rules
Although formally covered in upper sec, introduce the formulas for awareness:
sinAa=sinBb=sinCc,c2=a2+b2−2abcosC.
Practice Quiz
Check SOH-CAH-TOA recognition, diagram labelling, elevation problems, and bearings decomposition with the quiz below.
Try it yourself
Find the hypotenuse of a right triangle with adjacent side 9 cm and angle 28∘.
A ladder leans against a wall with its base 1.6 m from the wall and top 3.8 m above ground. Find the ladder length and angle of elevation.
Expected line length:1.62+3.82≈4.1m (angle of elevation ≈67.6∘).
Two observers stand 40 m apart on level ground. They observe the top of a pole with angles of elevation 32∘ and 48∘ respectively. Model the scenario and compute the pole height.
A yacht sails 12 km on a bearing of 040∘ then 8 km on 130∘. Calculate displacement from the starting point.
